Dynamic Reliability Assessment of Long-span Suspension bridges under stochastic traffic flow

For most existing bridges, supporting continuous traffic loads is the basic function. However, in addition to this load, bridges are exposed to environmental (Frangopol and Soliman, 2015 [1]), as well as various other complex loads, that are mostly random in nature, such as earthquake, flow-included loadings, wind and so on. All these loading conditions need to be considered and must satisfy the design criteria. In recent years, rapid growth of urban systems and the sprawling of large cities have resulted in significant traffic volume increase, and the corresponding vehicle weight on bridges. This new phenomenon, which for the most part may not have been accounted for when most bridges were originally constructed, has resulted in a threat to the safety of bridges (Han, et al., 2014 [2]). Wadhana and Hadipriono (2003) [3], concluded that the most frequent causes of bridge failures were attributed to overloading due to vehicles, besides floods and scouring. The vehicle overloading is the main human factor resulting in shortening the service life and even directly causing collapse of bridges in most counties (Deng, et al., 2015 [4]). In addition to the overloading vehicles, dynamic problems of long-span bridges have become increasingly significant with the increment in bridge span and flexibility. The sensitivity to dynamic wind actions increases with the reduction of modal frequencies (Xing et al., 2013 [5]). As reported in the literature, safety problems of existing bridges caused by vehicle loads due to sustainable growths of traffic volume and strong winds are becoming serious issues the with the fast development of urban areas. Therefore, the safety assessment of bridges is extremely important. If more accurate and more reliable safety assessment methodologies can be developed, it facilitates intervention strategies such as maintenance and reinforcement, which could be adopted to maintain the performance over certain thresholds according to the safety assessment results. Furthermore, since most bridges are throat of the traffic systems, their safety assurance is the foundation of economic development and national security. Suspension bridges, in particular, are widely used in highways crossing gorges, rivers, and gulfs, due to their superior advantages such as mechanical properties, large spanning ability, and appealing aesthetic appearance. The number and the span of suspension bridges are increasing gradually along with the advancements of computational capabilities and the construction technology. However, the safe performance of these long-span suspension bridges are facing numerous threats such as suffering from the incremental gross vehicle loads, strong winds, and other natural disasters (Brownjohn, 1997, [6]). There are numerous structural, mechanical and loading characteristic differences between suspension bridges and other short-span bridges, such as higher traffic volume, simultaneous presence of multiple vehicles, sensitivity to wind load, and inherent nonlinearities (Cai et al. 2015 [7]). The basic load combination methods, that are based on the currently used design codes and deterministic analysis methods may not be suitable for the safety assessment of suspension bridges, since interactions between the bridge, the loadings, and the environmental factors are ignored in the current analysis methods. On the other hand, the randomness of these loadings is not appropriately included. Furthermore, the environmental conditions of suspension bridges during their life-time are usually harsh which means that: i) suspension bridges are normally located in throat position of highways where busy traffic flow and heavy vehicles usually emerge; and ii) the environmental surroundings of suspension bridges produce strong winds which may cause a harsh structural vibration (Li et al. 2012 [8]). The large deformation and strong vibration caused by the increasing vehicle load and strong wind load directly threaten the safety of bridges and the comfort of passengers (Zhou and Chen, 1996 [9]). Considering that the two most important and common live loads acting on a bridge, namely the traffic flow and the wind load, that are the main cause of a bridge failure, are inherently stochastic in nature, this demonstrates the random vibration analysis of suspension bridge girders possesses great significance for better understanding the probabilistic dynamic reliability assessment and probabilistic dynamic performance of suspension bridges. Furthermore, the following dynamic reliability assessment for in service